Annihilators in the bidual of generalized group algebra of a discrete group
| Autor: | Singh, Lav Kumar |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Complex Analysis and Operator Theory, Vol 18, 68(2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11785-024-01506-4 |
| Popis: | In this short note, the second dual of generalized group algebra $(\ell^1(G,\mathcal A),\ast)$ equipped with both Arens products is investigated, where $G$ is any discrete group and $\mathcal A$ is a Banach algebra containing a complemented algebraic copy of $(\ell^1(\mathbb N),\bullet)$. We give an explicit family of annihilators(w.r.t both the Arens product) in the algebra $\ell^1(G,\mathcal A)^{**}$, arising from non-principal ultrafilters on $\mathbb N$ and which are not in the topological center. As a consequence, we also deduce the fact that $\ell^1(G,\mathcal A)$ is not Strongly Arens irregular. Comment: Major changes done in accordance with the referee report |
| Databáze: | arXiv |
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